Quizbank/College Physics Sem 1

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Wright State University Lake Campus

College Physics Sem 1

This unit has 5 exams (tests) that can viewed by clicking the links (e.g., T1). They are classroom-ready exams based on the collection of quizzes shown below each exam. The fraction indicates the ratio of the number of questions randomly selected to the number of questions on each quiz. Students can access these quizzes using either the (uneditable) permalink or directly via links to subpages of QB. Students and instructors can also view all at /All. Ideas for use by instructors can be found at Quizbank/Instructions.

Quizbank/College Physics Sem 1/T1

Test is Wed 17 Sep 2018

2/4 from Special:Permalink/1828918 to QB/a02_1Dkinem_definitions
3/4 from Special:Permalink/1863423 to QB/a02_1Dkinem_equations
5/12 from Special:Permalink/1863384 to QB/b_motionSimpleArithmetic
3/4 from Special:Permalink/1863096 to QB/a03_2Dkinem_2dmotion
2/4 from Special:Permalink/1863115 to QB/a03_2Dkinem_smithtrain

00-Mathematics_for_this_course

Measured in radians, $\theta =s/r$ defines angle (in radians), where s is arclength and r is radius. The circumference of a circle is $C_{\odot }=\,2\pi r$ and the circle's area is $A_{\odot }=\,\pi r^{2}$ is its area. The surface area of a sphere is $A_{\bigcirc }=4\pi r^{2}$ and sphere's volume is $V_{\bigcirc }={\frac {4}{3}}\pi r^{3}$

A vector can be expressed as, ${\vec {A}}=A_{x}\,{\hat {i}}+A_{y}\,{\hat {j}}$ , where $A_{x}=A\cos \theta$ , and $A_{y}=A\sin \theta$ are the x and y components. Alternative notation for the unit vectors $({\hat {i}},{\hat {j}})$ include $({\hat {x}},{\hat {y}})$ and $({\widehat {e_{1}}},{\widehat {e_{2}}})$ . An important vector is the displacement from the origin, with components are typically written without subscripts: ${\vec {r}}=x{\hat {x}}+y{\hat {y}}$ . The magnitude (or absolute value or norm) of a vector is is $A\equiv |{\vec {A}}|={\sqrt {A_{x}^{2}+A_{y}^{2}}}\quad$ , where the angle (or phase), $\theta$ , obeys $\tan \theta =y/x$ , or (almost) equivalently, $\theta =\arctan {(y/x)}\quad$ . As with any function/inverse function pair, the tangent and arctangent are related by $\tan(\tan ^{-1}{\mathcal {X}})={\mathcal {X}}$ where ${\mathcal {X}}=y/x$ . The arctangent is not a true function because it is multivalued, with $\tan ^{-1}(\tan \theta )=\theta \;or\;\theta +\pi$ .

The geometric interpretations of ${\vec {A}}+{\vec {B}}={\vec {C}}$ and ${\vec {B}}={\vec {C}}-{\vec {A}}$ are shown in the figure. Vector addition and subtraction can also be defined through the components: ${\vec {A}}+{\vec {B}}={\vec {C}}\Leftrightarrow$ $A_{x}+B_{x}=C_{x}$ AND $A_{y}+B_{y}=C_{y}$

01-Introduction

1 kilometer = .621 miles and 1 MPH = 1 mi/hr ≈ .447 m/s
Typically air density is 1.2kg/m³, with pressure 10⁵Pa. The density of water is 1000kg/m³.
Earth's mean radius ≈ 6371km, mass ≈ 6×10²⁴
kg, and gravitational acceleration = g ≈ 9.8m/s²
Universal gravitational constant = G ≈ 6.67×10⁻¹¹
m³·kg⁻¹·s⁻²
Speed of sound ≈ 340m/s and the speed of light = c ≈ 3×10⁸m/s
One light-year ≈ 9.5×10¹⁵m ≈ 63240AU (Astronomical unit)
The electron has charge, e ≈ 1.6 × 10⁻¹⁹C and mass ≈ 9.11 × 10^-31kg. 1eV = 1.602 × 10^-19J is a unit of energy, defined as the work associated with moving one electron through a potential difference of one volt.
1 amu = 1 u ≈ 1.66 × 10^-27 kg is the approximate mass of a proton or neutron.
Boltzmann's constant = k_B≈ 1.38 × 10^-23 J K⁻¹ , and the gas constant is R = N_Ak_B≈8.314 J K⁻¹ mol⁻¹, where N_A≈ 6.02 × 10²³ is the Avogadro number.
$k_{\mathrm {e} }={\frac {1}{4\pi \varepsilon _{0}}}\,$ ≈ 8.987× 10⁹ N·m²·C⁻² is a fundamental constant of electricity; also $\varepsilon _{0}={\frac {1}{4\pi k_{\mathrm {e} }}}\,$ ≈ 8.854 × 10⁻¹² F·m⁻¹ is the vacuum permittivity or the electric constant.
$\mu _{0}\,$ = 4π × 10⁻⁷ NA ≈ 1.257 × 10⁻⁶ N A (magnetic permeability) is the fundamental constant of magnetism: ${\sqrt {\varepsilon _{0}\mu _{0}}}=1/c$ .
$\hbar$ = h/(2π) ≈ 1.054×10⁻³⁴ J·s the reduced Planck constant, and $a_{0}={\frac {\hbar ^{2}}{k_{e}m_{e}e^{2}}}$ ≈ .526 × 10⁻¹⁰ m is the Bohr radius.

Two dimensional kinematics

Difference is denoted by $d{\mathcal {X}}$ , $\delta {\mathcal {X}}$ , or the Delta. $\Delta {\mathcal {X}}={\mathcal {X}}_{f}-{\mathcal {X}}_{i}$ or ${\mathcal {X}}-{\mathcal {X}}_{0}$ . Average, or mean, is denoted by ${\bar {\mathcal {X}}}=\langle {\mathcal {X}}\rangle ={\mathcal {X}}_{\text{ave}}=\Sigma {\mathcal {X}}_{i}{\mathcal {/}}N\ {\text{or}}\ \Sigma {\mathcal {P}}_{i}{\mathcal {X}}_{i}$ , where ${\mathcal {N}}$ is number and ${\mathcal {P}}_{i}$ are probabilities. The average velocity is ${\bar {v}}=\Delta x/\Delta t$ , and the average acceleration is ${\bar {a}}=\Delta v/\Delta t$ , where $x$ denotes position. In CALCULUS, instantaneous values are denoted by v(t)=dx/dt and a=dv/dt=d²x/dt².

The equations of motion for uniform acceleration are: $x=x_{0}+v_{0}t+{\tfrac {1}{2}}at^{2}$ , and, $v=v_{0}+at$ . Also, $v^{2}=v_{0}^{2}+2a\left(x-x_{0}\right)$ , and, $x-x_{0}={\tfrac {1}{2}}(v_{0}+v)={\bar {v}}t$ . Note that ${\bar {v}}={\tfrac {1}{2}}(v_{0}+v)$ only if the acceleration is uniform.

03-Two-Dimensional_Kinematics

$x=x_{0}+v_{0x}\Delta t+{\frac {1}{2}}a_{x}\Delta t^{2}$	$v_{x}=v_{0x}+a_{x}\Delta t$	$v_{x}^{2}=v_{x0}^{2}+2a_{x}\Delta x$
$y=y_{0}+v_{0y}\Delta t+{\frac {1}{2}}a_{y}\Delta t^{2}$	$v_{y}=v_{0y}+a_{y}\Delta t$	$v_{y}^{2}=v_{x0}^{2}+2a_{y}\Delta y$

$v^{2}=v_{0}^{2}+2a_{x}\Delta x+2a_{y}\Delta y$ ...in advanced notation this becomes $\Delta (v^{2})=2{\vec {a}}\cdot \Delta {\vec {\ell }}$ .

In free fall we often set, a_x=0 and a_y= -g. If angle is measured with respect to the x axis:

$v_{x}=v\cos \theta$ $v_{y}=v\sin \theta$ $v_{x0}=v_{0}\cos \theta _{0}$ $v_{y0}=v_{0}\sin \theta _{0}$

The figure shows a Man moving relative to Train with velocity, ${\vec {v}}_{M|T}$ , where the velocity of the train relative to Earth is, ${\vec {v}}_{T|E}$ is the velocity of the Train relative to Earth. The velocity of the Man relative to Earth is,

$\underbrace {{\vec {v}}_{M|E}} _{50\;km/hr}=\underbrace {{\vec {v}}_{M|T}} _{10\;km/hr}+\underbrace {{\vec {v}}_{T|E}} _{40\;km/hr}\,$ If the speeds are relativistic, define u=v/c where c is the speed of light, and this formula must be modified to: $u_{A|O}={\frac {u_{A|O'}+u_{O'|O}}{1+(u_{A|O\,'})(u_{O\,'|O})}}$